MATH 145 Section 003: Honors Calculus I

First course in the three-part basic calculus sequence for students majoring in mathematics, science, or engineering.  Topics include limits, continuity, differentiation, applications of differentiation, and integration.  Applications of the derivative are covered in detail, including approximations of errors using differentials, maxima and minima problems, curve sketching, optimization problems, and Newton's Method.  Topics on integration include Riemann sums, properties of definite integrals, integration by substitution, and integrals involving logarithmic, exponential, trigonometric, inverse trigonometric, and hyperbolic functions.

LEARNING OUTCOMES FOR 100- AND 200-LEVEL COURSES:

1. Students will be able to identify key concepts in the arts, sciences, humanities, or mathematics to provide a broad perspective.
2. Students will be able to demonstrate effective written communication skills.

LEARNING OUTCOMES FOR THIS COURSE:

1. Students will develop a basic understanding of the concepts of calculus and be able to apply them to real situations.
2. Students will be able to find limits of functions.
3. Students will be able to calculate (and simplify) derivatives involving rational, exponential, trigonometric, inverse trigonometric, and hyperbolic functions.
4. Students will be able to apply derivatives to various applications including optimization problems, linear approximation, and curve sketching.
5. Students will be able to calculate (and simplify) integrals using some basic techniques of integration.
6. Students will be able to use integration to find the area of certain types of planar regions.